Effective and deadly are not at all the same thing.
Grenades can definitely kill at very close proximity, but their big advantage is the shrapnel and blast/shock effect (the famed German "potato smasher" grenade is actually a concussion weapon, doing its work with blast effect and not fragmentation, there was a separate cover, the splinterring, that could be added to change it to a fragmentation weapon). Movies make the basic grenade look like a satchel charge, they aren't.
What a grenade will do, very effectively, is wound and disorientate everyone not under cover within a 15-30 meter radius in the case of fragmentation grenade (with frags going as far as 200 meters), and 2-8 meters for a concussion grenade. Deaths are generally are at very close range, 2-3 meters, or if one is unlucky enough to catch a splinter in a vital bit of real estate or in a position where aid isn't available and and the victim slowly bleeds out. Wounding/concussing is the idea effect for a weapon in that it both greatly reduces the effectiveness of the enemy, especially in a fixed position, and in that is causes enormous logistical impact on the enemy when the have to provide care for a dozen shrapnel wounded troops or troops with traumatic amputations.
Grenades will also have a increased lethality when deployed into a closed space such as a bunker or inside a vehicle, the enclosed space maximizes the concussive effect and increases the likelihood of a lethal injury/wound.
Nasty little critters.